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Data Visualization using Linear and Non-linear Dimensionality Reduction Methods

  • Kim, Junsuk (Center for Neuroscience Imaging Research, Institute for Basic Science) ;
  • Youn, Joosang (Dept. of Industrial ICT Engineering, Dong-Eui University)
  • Received : 2018.10.12
  • Accepted : 2018.11.21
  • Published : 2018.12.31

Abstract

As the large amount of data can be efficiently stored, the methods extracting meaningful features from big data has become important. Especially, the techniques of converting high- to low-dimensional data are crucial for the 'Data visualization'. In this study, principal component analysis (PCA; linear dimensionality reduction technique) and Isomap (non-linear dimensionality reduction technique) are introduced and applied to neural big data obtained by the functional magnetic resonance imaging (fMRI). First, we investigate how much the physical properties of stimuli are maintained after the dimensionality reduction processes. We moreover compared the amount of residual variance to quantitatively compare the amount of information that was not explained. As result, the dimensionality reduction using Isomap contains more information than the principal component analysis. Our results demonstrate that it is necessary to consider not only linear but also nonlinear characteristics in the big data analysis.

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Fig. 1. Overview of neural data visualization procedure

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Fig. 2. fMRI experimental design

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Fig. 3. Anatomical region of primary somatosensory cortex

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Fig. 4. Visualization results using two different dimensionality reduction methods

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Fig. 5. Performance comparison using residual variances

References

  1. Kim, Y, Cho, KH, "Big Data and Statistics", Journal of the Korean Data and Information Science Society, Vol. 24, No. 5, pp.959-974, 2013. https://doi.org/10.7465/jkdi.2013.24.5.959
  2. Park, H-J, Gwon, Y-H, An, Y-M, "Big Data and Its Refining Technology", Korean Society of Computer Information Review, Vol. 21, No. 1, pp.1-8, 2013.
  3. Kim, ST, "3 Elements for the Successful Big Data Usage: Resources, Technology, Man Power", IT & Future Strategy, Vol. 3. 2012.
  4. Pereira, F. and Botvinick, M., "Machine learning classifiers and fMRI: a tutorial overview." Neuroimage, Vol.45, No.1, pp.S199-S209, 2009. https://doi.org/10.1016/j.neuroimage.2008.11.007
  5. Lee, J-H, Je, M-G, Jo, M-J, Son, H-S, "Trends of Big Data Use in Medical Field", Information and Communications Magazine, Vol. 32, No. 1, pp.63-75, 2014.
  6. Choe, G-S, Ham Y-G, Kim S-H, "Visualization of Big Data", Korean Society of Computer Information Review, Vol. 21, No. 1, pp.33-43, 2013.
  7. Pearson, K., "On Lines and Planes of Closest Fit to Systems of Points in Space." Philosophical Magazine, Vol.2, No.11, pp.559-572, 1901.
  8. Bronstein AM, Bronstein MM, Kimmel R, "Generalized multidimensional scaling: a framework for isometry-invar iant partial surface matching." Proc. Natl. Acad. Sci. U.S.A., Vol.103, No.5, pp1168-1172, 2006. https://doi.org/10.1073/pnas.0508601103
  9. Tenenbaum, J.B., De Silva, V. and Langford, J.C., "A global geometric framework for nonlinear dimensionality reduction." Science, Vol.290, No.5500, pp.2319-2323, 2000. https://doi.org/10.1126/science.290.5500.2319
  10. Gorban, A. N., Kégl, B., Wunsch, D. C., and Zinovyev, A. Y., Principal manifolds for data visualization and dimension reduction, Springer, Berlin-Heidelberg, 2008.
  11. Bellman. R. Adaptive control processes: A guided tour, Princeton University Press, Princeton, 1961.
  12. Hastie, T., Tibshirani, R. and Friedman, J., Overview of supervised learning. In The elements of statistical learning, Springer, New York, 2009.
  13. Hu, J., Tian, J. and Yang, L., "Functional feature embedded space mapping of fMRI data." In Engineering in Medicine and Biology Society (EMBS), pp.1014-1017, 2006.
  14. Martuzzi, R., Zwaag, W., Farthouat, J., Gruetter, R. and Blanke, O., "Human finger somatotopy in areas 3b, 1, and 2: a 7T fMRI study using a natural stimulus." Human brain mapping, Vol.35, No.1, pp.213-226, 2014. https://doi.org/10.1002/hbm.22172
  15. Hannachi, A. and Turner, A.G., "Isomap nonlinear dimensionality reduction and bimodality of Asian monsoon convection." Geophysical Research Letters, Vol.40, No.8, pp.1653-1658, 2013. https://doi.org/10.1002/grl.50351
  16. Zhang, C., Wang, J., Zhao, N. and Zhang, D., "Reconstruction and analysis of multi-pose face images based on nonlinear dimensionality reduction." Pattern Recognition, Vol.37, No.2, pp.325-336, 2004. https://doi.org/10.1016/j.patcog.2003.07.005
  17. Yang, J., Wang, H., Ding, H., An, N. and Alterovitz, G., "Nonlinear dimensionality reduction methods for synthetic biology biobricks' visualization." BMC bioinformatics, Vol.18, No.47, pp.1-10, 2017.